Question

( a + b ) ( a³ - b³ ) ÷ a² - b² =

Answer 1

Answer:

We know two formulas, that is:

a³-b³= (a-b)(a²+b²+ab)

a²-b²= (a+b)(a-b)

So putting the evaluations of the formulas in the given one.

(a³-b³)/(a²-b²)

= (a-b)(a²+b²+ab)/(a+b)(a-b)

= (a²+b²+ab)/(a+b)

We know

(a+b)²=a²+b²+2ab

a²+b²=(a+b)²-2ab

So,

= {[(a+b)²-2ab]+ab}/(a+b)

{(a+b)²-2ab+ab}/(a+b)

{(a+b)²-ab}/(a+b)

(a+b)²/(a+b) - ab/(a+b)

(a+b) - ab/(a+b)